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Given a Lie algebra \(\mathfrak{g}\) over a ring \(R\), the universal enveloping algebra of \(\mathfrak{g}\), \(U(\mathfrak{g})\), is an associative \(R\)-algebra which contains \(\mathfrak{g}\) as a sub algebra. It is constructed by taking the free associative \(R\)-algebra over \(\mathfrak{g}\), \(R\langle \mathfrak{g}\rangle=A\), and taking the quotient by the sub-module spanned by: \(\{x+_Ay-(x+_\mathfrak{g}y),\:r\cdot_Ax-(r\cdot_{\mathfrak{g}}x,\:xy-yx-[x,y]|r\in R,\:x,y\in \mathfrak{g}\}\).